Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 15.4461705338 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.258901233\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.376587517\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.183070818\)
\(a_{11}=+0.083259500\) \(a_{12}=-0.288675135\) \(a_{13}=-1.094825045\) \(a_{14}=-0.266287587\) \(a_{15}=+0.149476697\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.188136038\) \(a_{18}=-0.235702260\) \(a_{19}=-1.406442179\) \(a_{20}=-0.129450617\)
\(a_{21}=-0.217422904\) \(a_{22}=-0.058873357\) \(a_{23}=-0.644061232\) \(a_{24}=+0.204124145\) \(a_{25}=-0.932970151\)
\(a_{26}=+0.774158213\) \(a_{27}=-0.192450090\) \(a_{28}=+0.188293759\) \(a_{29}=+1.867282588\) \(a_{30}=-0.105695986\)
\(a_{31}=+1.943806902\) \(a_{32}=-0.176776695\) \(a_{33}=-0.048069895\) \(a_{34}=+0.133032268\) \(a_{35}=-0.097498973\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.021057695\) \(a_{38}=+0.994504802\) \(a_{39}=+0.632097534\) \(a_{40}=+0.091535409\)
\(a_{41}=+0.303366831\) \(a_{42}=+0.153741210\) \(a_{43}=-1.087792765\) \(a_{44}=+0.041629750\) \(a_{45}=-0.086300411\)
\(a_{46}=+0.455420065\) \(a_{47}=+0.830903414\) \(a_{48}=-0.144337567\) \(a_{49}=-0.858181842\) \(a_{50}=+0.659709521\)
\(a_{51}=+0.108620392\) \(a_{52}=-0.547412522\) \(a_{53}=+0.950906290\) \(a_{54}=+0.136082763\) \(a_{55}=-0.021555987\)
\(a_{56}=-0.133143794\) \(a_{57}=+0.812009771\) \(a_{58}=-1.320368180\) \(a_{59}=-0.629236390\) \(a_{60}=+0.074738348\)
\(a_{61}=+1.226843019\) \(a_{62}=-1.374479042\) \(a_{63}=+0.125529172\) \(a_{64}=+0.125000000\) \(a_{65}=+0.283451554\)
\(a_{66}=+0.033990549\) \(a_{67}=+0.818743500\) \(a_{68}=-0.094068019\) \(a_{69}=+0.371848926\) \(a_{70}=+0.068942185\)
\(a_{71}=+0.429235900\) \(a_{72}=-0.117851130\) \(a_{73}=-1.069562000\) \(a_{74}=-0.721996820\) \(a_{75}=+0.538650568\)
\(a_{76}=-0.703221090\) \(a_{77}=+0.031354488\) \(a_{78}=-0.446960453\) \(a_{79}=+0.530221999\) \(a_{80}=-0.064725308\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.214512743\) \(a_{83}=+1.611938998\) \(a_{84}=-0.108711452\) \(a_{85}=+0.048708652\)
\(a_{86}=+0.769185641\) \(a_{87}=-1.078076105\) \(a_{88}=-0.029436679\) \(a_{89}=+0.664800000\) \(a_{90}=+0.061023606\)
\(a_{91}=-0.412297445\) \(a_{92}=-0.322030616\) \(a_{93}=-1.122257438\) \(a_{94}=-0.587537439\) \(a_{95}=+0.364129615\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.369998932\) \(a_{98}=+0.606826200\) \(a_{99}=+0.027753167\) \(a_{100}=-0.466485076\)

Showing 100 of 102 available coefficients

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